This “hands free” access system is known to those skilled in the art. It generally consists of an electronic control unit installed in the vehicle, one or more radio-frequency (RF) antennas situated on the vehicle and an identification badge or remote control comprising an RF antenna and an associated electronic circuit carried by the user.
An identifying exchange between the badge and the vehicle by the intermediary of the RF antennas allows the identification of the badge by the vehicle and the triggering of the locking or unlocking of the openings by the latter.
In order to carry out the radio communication with the vehicle, the portable radio communication device D comprises, in a insulating casing B (see FIG. 1), a printed circuit 30 upon which there is a radio-frequency antenna A electrically connected to an associated electronic transmitter/receiver circuit 50 itself comprising:                a receiver unit Rx making it possible to receive the data coming from the vehicle, transmitted by radio-frequency waves,        a transmitter unit Tx making it possible to send data to the vehicle by radio-frequency waves,        a gain amplifier Gx, associated with the gain G of the antenna A,        a microcontroller 10 managing the transmission/reception of the data,        an impedance adapting unit 20, generally a network of capacitive and inductive elements in order to adapt the impedance of the antenna A,        a switch S making it possible to select the receiver unit Rx or the transmitter unit Tx depending on the phase in which the communication of the antenna A is: receiving data or transmitting data.        
The switch S and the gain amplifier Gx are controlled by the microcontroller 10.
The portable device D is powered by a battery (not shown) mounted on the printed circuit 30.
This portable radio communication device D is known to those skilled in the art and will not be described in more detail here.
The gain G of the antenna A of the portable device D is determined by the effective area of the antenna A and therefore of the space allocated to it in the insulating casing B. As the geometry of the antenna A is fixed, said gain G is also fixed.
As for the gain amplifier Gx, this makes it possible to adapt by software means the gain Gtot of the portable device D during the transmission of data by said antenna A, according to the type of application of the portable device D, where Gtot=Gx+G.
The total gain is defined by:Gtot=Gx+G. 
where:
Gx: Gain of the gain amplifier,
G: Gain of the antenna A.
Most often, the gain Gtot of the portable device D is determined according to the legislation in force concerning the authorized maximum power of radio-frequency transmissions for the country in which the vehicle is marketed.
There are however notable differences from country to country between the maximum power values authorized for the transmission of radio-frequency waves.
In order to reduce the complexity in the production of the portable device D, the gain Gtot is generally adjusted according to the most severe legislation.
Thus the effective area, that is to say the gain G of the antenna A and a maximum gain Gxmax of the gain amplifier Gx are previously fixed for the maximum radiated power authorized by the most severe legislation.
The total gain Gtot can then be adjusted using the gain amplifier Gx, within the limit of its maximum gain value Gxmax. The maximum value of the gain Gxmax is determined as a function of the maximum acceptable electrical consumption of the portable device D.
For certain countries in which the legislation concerning the maximum authorized radiated power of radio-frequency transmissions is less severe, the total gain Gtotal of the portable device D is not therefore adapted; in fact it could be greater than that which is previously adjusted in said portable device D.
As previously explained:                the gain G of the antenna A is fixed and is limited, because the space allocated in the portable device D for said antenna A is restricted        the electrical consumption of the portable device D itself limits the value of the maximum gain Gxmax of the gain amplifier Gx.        
By increasing the transmission power of the radio-frequency waves (that is to say by increasing the total gain Gtot), the detection of said waves by the vehicle and therefore the reliability of the “hands-free” access system is improved.
It will be understood that there is a need to have a gain G of the antenna A greater that that currently available in order to increase the total gain Gtot of the portable device.